Chapter 7Confidence Intervals

In the days leading up to the 2012 presidential election, my brother called me fired up about some recent polling results. The polling agency reported that the percentage of Americans who were planning to vote for Barack Obama on November 6 – election day – was 49%. Roughly 200 million Americans were registered to vote in the last election and the poll results were based on – wait for it – 1300 people.1 My brother quickly dismissed the results, arguing that there is no way a sample of 1300 could accurately reflect the preferences of a population of 200 million voters. “I mean, that's a tiny fraction of Americans that was sampled, so it must be bogus.” He is right, but only about the sample size being small. The sample is roughly 0.00065% of the population of interest. That is a small sample relative to the population size. I was not part of that sample, and if I were a betting man, I would wager that you were not either. But, here is the thing, he was probably wrong about the results being bogus. In fact, not only was a sample size of 1300 adequate for the election polling, it was deliberately chosen as the target sample size.

Let us be clear though. The actual number of registered voters who planned on voting for Obama was probably not exactly 49% like the report found. The chance of that happening – a sample value equaling the true value – is extremely low. It is effectively zero. The polling agency, of course, understands this and that is why ...

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